It is shown that the degree of polarization analysis is useful to find objective spectra of exoplanets immersed in noisy stellar spectra. We report the laboratory experiment of polarization differential objective spectroscopy with a four-quadrant polarization mask coronagraph, where partially polarized planetary signal is expected to be discerned from unpolarized stellar noise. The detection of the planet signal is impeded by the stellar noise remained after subtracting mutually orthogonally polarized components of light. We distinguish clearly the planetary spectrum by use of the degree of polarization. We also show the refinement of the spectrum of the planet model.
© 2007 Optical Society of America
The search for extrasolar planets is being under way and up to now more than 240 exoplanets have been discovered by using indirect detection methods. Various kinds of indirect detection methods are available, such as radial velocity method, photometry, microlensing, astrometry, etc. . Development of direct detection methods is crucial to characterize exoplanets. By using direct detection methods more information about exoplanets can be obtained from their spectra. However, the extremely high contrast and high-spatial resolution are needed to realize the direct detection. The difficulty lies in overwhelming starlight compared to the dim light from the planet. Starlight should be sufficiently suppressed to enable the detection of the planetary signal.
Several nulling methods have been proposed for achieving high-contrast imaging, such as nulling interferometry [2, 3, 4, 5, 6] and nulling coronagraph [7, 8, 9, 10, 11, 12]. One of the useful techniques, which can be applied to elimination of starlight and obtaining direct images, is a differential imaging technique [13, 14, 15, 16, 17]. The spectral differential imaging  is based on detecting the difference between the absorption line contained in the planetary light and the neighboring continuum. Then, the starlight is suppressed in the subtracted image and the planet image can be discerned. In synchronous interferometric speckle subtraction  the speckles caused by starlight, which are coherent with the starlight, are separated from the incoherent planetary light. The angular differential imaging  is a technique to reduce quasistatic speckle noise. A sequence of images is acquired with a slow rotation of the field of view, where a reference point-spread function (PSF) is smeared azimuthally. The smeared PSF is used to remove the quasistatic speckle noise. The polarimetric differential imaging [14, 15], which we use in the present research, is based on clipping unpolarized stellar light from partially polarized planetary light. The starlight is expected to be unpolarized, while the light that is reflected and scattered by the planet is generally partially polarized. The difference between mutually orthogonally polarized (s- and p-) components of light leaves only the planetary signal, because unpolarized starlight noise could be cancelled out. Polarimetry is particularly effective when the planetary phase angle, the angle between the star and the observer as seen from the center of the planet, is close to 90°, namely a face-on situation. For example, a numerical simulation of flux and polarization spectra  for Jupiter-like extrasolar planets shows that the degree of polarization of the planet can reach about 60 % at a planetary phase angle of 90°. It should be noted that the radial velocity method, a powerful indirect method, cannot be applicable to an exoplanet at the planetary phase angle of 90°.
The polarization differential technique has been applied to objective spectroscopy with a nulling stellar coronagraph . This coronagraph based on polarization interferometry works for wide range of wavelength . The nulling coronagraph combined with a spectropolarimeter makes it possible to obtain a direct image of an object and its spectrum with s- and p-polarized components. The difference of the spectra between s- and p-polarized components reveals only the planetary spectrum, in the ideal case, because both components of polarization are equal in unpolarized starlight. In practice, however, it is impossible to cancel completely the starlight and stellar noise remains in the differential image and spectrum.
Stellar noise exceeds the planetary signal with increasing intensity contrast between a star and its planet, and it becomes impossible to distinguish the planetary signal from the stellar noise. In this paper we alleviate this problem by conducting a polarization degree analysis of the differential spectra. The degree of polarization of a planet can surpass definitely the polarization degree of noisy starlight. Thereby the planetary spectrum reveals clearly.
We use a liquid-crystal variable retarder (LCVR) to change and measure s- and p-polarization components. It is shown that the calibration of spectral transmittance of our coronagraphic system refines the degree of polarization of the planetary spectrum. The refined spectrum of a planet model is also shown. In § 2 we describe our optical setup, differential polarization method and experimental procedure. The experimental results are shown in § 3, and § 4 is our conclusions.
2. Method and experiment
Figure 1 shows our optical setup for polarization differential objective spectroscopy. It consists of an LCVR as a polarization modulator, nulling coronagraphic optics and an objective spectrometer.
The principle of our nulling coronagraph is based on polarization interference . A four-quadrant polarization mask (FQPoM) is placed between two polarizers and an image of a star model is formed in the center of the mask. The FQPoM is composed of four half-wave plates with each optical axis as shown in Fig. 1. In contrast with a four-quadrant phase mask  the use of the polarization mask makes it possible to realize achromatic interference. The suppression of starlight is achieved by destructive interference that occurs when the optical axes of the polarizers before and after the FQPoM are mutually orthogonal as in Fig. 1. The destructive interference is observed inside the Lyot-stop. Two orthogonal polarization components of light of an object model are needed to recover the planetary signal. For the polarization modulation we use the LCVR whose retardation is adjusted by changing the applied voltage. The optical axis of the LCVR is set to 45°. By setting the retardation of the LCVR to the state of a wave or a half-wave plate we can take the s- and p-polarization components. In our experiment the planet light is made partially polarized by a set of tilted glass plates, while the starlight is unpolarized. We can delete unpolarized stellar noise and extract the planetary signal by subtraction of one polarization component from the other.
To simulate stellar and planetary light we use two xenon lamps. The same type of a xenon lamp was chosen to make the spectra similar, because the planetary light is reflected and scattered light of starlight by the planet and the spectra of the star and its planet become similar. To characterize the planetary light we made an artificial absorption line around λ=630 nm by an interference filter. A short-pass filter cuts light with wavelength longer than 800 nm. The light beams are directed to the optical bench with optical fibers. Collimator lenses collimate the beams from the planetary and the stellar model sources. A set of glass plates make the planetary light partially polarized. In our experiment the degree of polarization of the planetary light was set to about 50 %. The planetary and stellar light beams are combined with a cube beam splitter (CBS) and then led to the polarization modulator and coronagraphic optics. The change of the LCVR retardation between 2π and π is realized by switching the applied voltage to 2.25 and 3.40 V rms, respectively.
The entrance pupil is a circular aperture with a diameter of 2.5 mm. A lens (focal length of 1000 mm) forms the images of the stellar and planetary models on the plane of the FQPoM. The stellar image is formed on the center of the FQPoM. The planetary image is formed on one of FQPoM’s zones. The position of the planet is adjustable by tilting a mirror. A lens (focal length of 500 mm) reimages the entrance pupil on the Lyot stop plane with a magnification of 1/2. Then, the diameter of the reimaged pupil becomes 1.25 mm. The Lyot stop is a circular pupil with a diameter of 1.0 mm, which is 80 % of the reimaged entrance pupil. The sharp-cut filter removes light with wavelength shorter than 540 nm.
A blazed reflection grating and a camera lens (focal length of 80 mm) form the objective spectra, which are detected by an electron-multiplier CCD (EMCCD) camera (512×512 pixels with a pixel of 16×16 µm2). The EMCCD camera has high sensitivity that permits to detect a faint signal. We used a blazed grating with 600 lines mm-1. The available observational range of the spectra is about 150 nm centered on 630 nm. By tilting the grating we can observe the 0th order diffraction image. We took the direct image with 128×128 pixels and the objective spectra with 512×128 pixels. By using the direct image we measure the intensity contrast between the planetary and the stellar light and also adjust the angular distance. We present experimental results obtained with an intensity contrast of 7×10-5 and angular separation of 4.8 λ/D.
Figures 2(a) and 2(b) show the s- and p-polarized components of the destructively interfered image, respectively. Figure 2(c) shows the differential image through subtraction of these two images. The absolute values are shown in Fig. 2(c). The intensity of the noise on the differential image appears similar to the s- and p-polarized images, since each image is normalized to its maximum intensity. Actually the maximum intensity of the differential image is 100 times less than those of Figs. 2(a) and 2(b).
Figures 3(a) and 3(b) show the s- and p-polarized components of the objective spectra and 3(c) is their differential spectra. It is very hard to distinguish the spectrum of the planet on the differential spectra, because the intensity of stellar noise significantly exceeds that of the planetary signal even after the subtraction. We tackle this problem in the next section.
3. Representation of spectra with the degree of polarization
When the intensity ratio of a star to its planet increases, the ratio between the intensities of the speckle noise caused by the starlight and the planet increases too. Thus, the spectrum of the planet becomes invisible against the bright stellar noise. We conduct a polarization degree analysis of the differential spectra to detect the planetary signal.
The degree of polarization at the (i, j) pixel, qij is:
where Iwp ij is the intensity of the spectrum at the (i, j) pixel in case of the LCVR with a retardation of one wave (corresponding to s-polarization), and Ihwp ij is the one in case of the LCVR with a retardation of a half-wave (corresponding to p-polarization). Equation (1) corresponds to Q/I and a measurement of U/I is also needed not to miss linearly polarized components oriented at 45° and 135° from the p-axis, where I, Q, and U are the Stokes parameters. The degree of polarization takes a low value when the difference between the s- and p-polarization components is small compared to the intensity at that point. Thus, the degree of polarization of the planetary spectrum exceeds the degree of polarization of noisy starlight, because the planetary spectrum is partially polarized and the starlight is unpolarized. Even if the noisy starlight is partially polarized (mainly because of instrumental polarization), the degree of polarization of the noisy components becomes low because of the normalization by the intensity at each point. It should be noted that such instrumental polarization can be calibrated by observing an unpolarized reference star. By analyzing the degree of polarization of the differential spectra we can expect to reduce the contribution of the obstructive stellar noise and extract the planetary spectrum. Figure 4(a) shows the degree of polarization of the differential objective spectra. From the spectra represented with the degree of polarization we can recognize the planetary spectrum. However, the spectra with the degree of polarization contain too much stellar noise that appears also polarized. This is unreasonable. So we suspected that the cause could be incurred by the spectral transmittance characteristic of the LCVR.
We measured the spectral transmittance of our coronagraphic optics. The data were taken with the light of the star model. The light was directed to one zone of the four-quadrant mask and both polarization components were measured by changing the retardation of the LCVR. Such measurements were done with the other three zones of the FQPoM, and all zones had similar characteristics. Figure 5(a) shows the spectral transmittance of our coronagraphic optics in the cases of one wave (lower curve) and the half-wave (upper curve) retardations.
As can be seen from Fig. 5(a) the transmittances of the coronagraphic optics are different in the retardations of the LCVR. Therefore, the differential spectra can be refined by including this characteristic in the scaling factor k j for subtraction. The scaling factor k j is a function of wavelength (here wavelength indexed with j). The curve in Fig. 5(b) shows the spectral dependence of Twp/Thwp (Twp, Thwp: the transmittances of our coronagraphic optics with retardations of the LCVR in the states of a wave plate and a half-wave plate, respectively). This curve can be approximately fitted by a linear function. Then, the differential spectra can be corrected by using a linear function with wavelength for the scaling factor k i. Therefore, the subtraction of two polarization components I wp ij and I hwp ij of the objective spectra is
Then, the degree of polarization becomes
Figure 4(b) shows the degree of polarization of the calibrated differential spectra by using the linear scaling factor.
The planetary signal is well represented with this calibrated degree of polarization of the spectrum. Thereby we can detect the position of the planet and extract the planetary spectrum. It should be noted that the signs of the degree of polarization of the spectra happen to be opposite for the planetary light and the stellar noisy light. Instrumental polarization incurred the partial polarization to the light of stellar noise. In some cases the sign of the degree of polarization would be useful to discriminate clearly the planetary spectrum from noisy spurious spectra.
Figure 6(a) shows the planetary spectrum extracted from the differential spectrum in Fig. 3(c) (red curve), and the spectrum of the planetary model (green curve) which is measured without the LCVR and the starlight. The spectral transmittance of the LCVR affects the observed spectrum. The LCVR we used gives π-phase shift at a wavelength of 630 nm. For correcting the chromatic effect of the LCVR we measured the spectral transmittance as shown in Fig 6(b). Different from Fig. 5(a) the transmittances in Fig. 6(b) do not contain the effects of the FQPoM and the polarizers. As can be seen from Fig. 6(b) large deviations from the transmittance value at λ=630 nm occur in the short wavelength region. Thus, the spectrum is needed correction especially in the short wavelength region.
For calibration of the planetary spectrum we use the spectral transmittance of the LCVR shown in Fig. 6(b). Figure 6(c) shows the refined planetary spectrum (blue curve) and the spectrum of the planetary model without the LCVR and the starlight (green curve, the same as in (a)). The intensities on Figs. 6(a) and 6(c) are plotted with a linear scale. Comparing Figs. 6(a) with 6(c) the refined spectrum exhibits the overall feature of the planetary spectrum without the starlight. To estimate the improvement of the refined spectrum we calculated the rms (root-mean-square) errors of the extracted and the refined spectra. The rms errors were reduced by 22 % in the shorter wavelength region than the absorption line. The absorption line extracted from the differential spectrum becomes shallow because the difference between low values becomes always low and is affected by noise.
In this paper we have presented the laboratory demonstration of polarization differential objective spectroscopy with the FQPoM coronagraph. We conducted the experiments with a simulated star-planet system. In our experiments the intensity ratio of the planet to the star was 7×10-5 and the angular separation was 4.7 λ/D. When the intensity of the planet becomes small in comparison with the intensity of stellar noise, the detection of the planetary spectrum becomes difficult. We showed that the analysis of the degree of polarization of the measured differential spectra is useful to discriminate the planetary spectrum from the noisy spectra caused by the starlight. Then, we could identify the position of the planetary spectrum and extract the spectrum from the differential spectra with intense speckle noise. It is worth noticing that the degree of polarization can be higher at absorption lines than the adjacent continua according to the theoretical analysis by Stam, Hovenier, and Waters .
Since the LCVR has different spectral transmittance for a wave and a half-wave retardations we measured the transmittance of our coronagraphic optics to refine the spectra with the degree of polarization. The calibration of the planetary spectrum was performed by using the transmittance factor of the LCVR.
The differential spectropolarization method enables us to reconstruct the spectrum of the planet. Here we applied this method to a nulling stellar coronagraph with the FQPoM. It should be noted that the differential spectropolarization method can be used in the other types of stellar coronagraphs.
As pointed out by Breckingridge and Oppenheimer [21, 22], the instrumental polarization induced by telescope optics causes serious problems for a nulling stellar coronagraph. To make the nulling interference perfect, we must compensate for the instrumental polarization. Hong  has proposed an effective compensation technique using formbirefringence. However, further study would be needed to compensate for the instrumental polarization over a wider spectral region.
We are grateful to T. Yamamoto of the Institute of Low Temperature Science of Hokkaido University for providing an EMCCD camera. We thank N. Hashimoto of the Citizen Watch Company for supplying the FQPoM and LCVR to us. The research was supported by the Japan Society for the Promotion of Science under a Grant-in-Aid for Scientific Research (B) and by the National Astronomical Observatory of Japan.
References and links
2. N. Woolf and J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998). [CrossRef]
3. C. A. Beichman, N. J. Woolf, and C. A. Lindensmith, The Terrestrial Planet Finder (JPL Publication 99–3 Pasadena, CA, 1999).
4. E. Serabyn, J. K. Wallace, G. J. Hardy, E. G. H. Schmidtlin, and H. T. Nguyen, “Deep nulling of visible laser light,” Appl. Opt. 38, 7128–7132 (1999). [CrossRef]
5. N. Baba, N. Murakami, and T. Ishigaki, “Nulling interferometry by use of geometric phase,” Opt. Lett. 26, 1167–1169 (2001). [CrossRef]
6. A. Tavrov, R. Bohr, M. Totzeck, H. Tiziani, and M. Takeda, “Achromatic nulling interferometer based on a geometric spin-redirection phase,” Opt. Lett. 27, 2070–2072 (2002). [CrossRef]
7. F. Roddier and C. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997). [CrossRef]
8. P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. 141, 319–329 (2000).
9. N. Baba, N. Murakami, T. Ishigaki, and N. Hashimoto, “Polarization interferometric stellar coronagraph,” Opt. Lett. 27, 1373–1375 (2002). [CrossRef]
10. O. Guyon and F. Roddier, “A nulling wide field imager for exoplanets detection and general astrophysics,” Astron. Astrophys. 391, 379–395 (2002). [CrossRef]
11. G. A. Swartzlander Jr., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001). [CrossRef]
12. D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005). [CrossRef]
13. R. Racine, G. Walker, D. Nadeau, R. Doyon, and C. Marois, “Speckle noise and the detection of faint companions,” Publ. Astron. Soc. Pac. 111, 587–594 (1999). [CrossRef]
14. J. R. Kuhn, D. Potter, and B. Parise, “Imaging polarimetric observations of a new circumsteller disk system”, Astrophys. J. 553, L189–L191 (2001). [CrossRef]
15. N. Baba and N. Murakami, “A method to image extrasolar planets with polarized light,” Publ. Astron. Soc. Pac. 115, 1363–1366 (2003). [CrossRef]
16. O. Guyon. “Synchronous interferometric speckle subtraction,” Astrophys. J. 615, 562–572 (2004). [CrossRef]
17. C. Marois, D. Lafrenière, R. Doyon, B. Macintosh, and D. Nadeau, “Angular differential imaging: a powerful high-contrast imaging technique ,” Astrophys. J. 641, 556–564 (2006).
18. D. M. Stam, J. W. Hovenier, and L. B. F. M. Waters, “Using polarimetry to detect and characterize Jupiterlike extrasolar planets,” Astron. Astrophys. 428, 663–672 (2004). [CrossRef]
19. N. Murakami, N. Baba, Y. Tate, Y. Sato, and M. Tamura, “Polarization differential objective spectroscopy with nulling coronagraph,” Publ. Astron. Soc. Pac. 118, 774–779 (2006). [CrossRef]
20. D. Rouan, P. Riaud, A. Boccaletti, Y. Clenet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000). [CrossRef]
21. J. B. Breckinridge and B. R. Oppenheimer, “Polarization effects in reflecting coronagraphs for white-light applications in astronomy,” Astrophys. J. 600, 1091–1098 (2004). [CrossRef]
22. J. B. Breckinridge, “Image Formation in high contrast optical systems: the role of polarization,” Proc. SPIE 5487, 1337–1345 (2004). [CrossRef]
23. J. Hong, “Precision compensation for polarization anisotropies in metal reflectors,” Opt. Eng. 43, 1276–1277 (2004). [CrossRef]